So I believe everyone has the right to identify as they choose. If someone feels they are more female than their genitalia suggests or vice versa or if someone doesn't identify as a specific gender gender then I feel we live in a modern society which can be inclusive of everyone.
But
Given the number women who are murdered/raped/attacked by men. We (women) have the right to be safe and I would say that trumps the right to identify. So yes there should be womens spaces, and yes women should have their own category in sport. So what does that mean? Womens spaces, gender neutral spaces and mens spaces seems the most logical solution as it would also work for people who are gender neutral, none binary and pan gender. Surely that's the thing to be fighting for?